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2 years ago

Find the exterior angle

Mathematics

1 answer:

wel2 years ago

6 0

Check the picture below.

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In a right triangle ABC, CD is an altitude, such that AD=BC. Find AC, if AB=3 cm, and CD= 2 cm.

konstantin123 [22]

Consider right triangle ΔABC with legs AC and BC and hypotenuse AB. Draw the altitude CD.

1. Theorem: The length of each leg of a right triangle is the geometric mean of the length of the hypotenuse and the length of the segment of the hypotenuse adjacent to that leg.

According to this theorem,

$BC^2=BD\cdot AB.$

Let BC=x cm, then AD=BC=x cm and BD=AB-AD=3-x cm. Then

$x^2=(3-x)\cdot 3,\\ \\x^2=9-3x,\\ \\x^2+3x-9=0,\\ \\D=3^2-4\cdot (-9)=9+36=45,\\ \\\sqrt{D}=\sqrt{45}=3\sqrt{5},\\ \\x_1=\dfrac{-3-3\sqrt{5} }{2}0.$

Take positive value x. You get

$AD=BC=\dfrac{-3+3\sqrt{5} }{2}\ cm.$

2. According to the previous theorem,

$AC^2=AD\cdot AB.$

Then

$AC^2=\dfrac{-3+3\sqrt{5} }{2}\cdot 3=\dfrac{-9+9\sqrt{5} }{2},\\ \\AC=\sqrt{\dfrac{-9+9\sqrt{5} }{2}}\ cm.$

Answer: $AC=\sqrt{\dfrac{-9+9\sqrt{5} }{2}}\ cm.$

This solution doesn't need CD=2 cm. Note that if AB=3cm and CD=2cm, then

$CD^2=AD\cdot DB,\\ \\2^2=AD\cdot (3-AD),\\ \\AD^2-3AD+4=0,\\ \\D$

This means that you cannot find solutions of this equation. Then CD≠2 cm.

8 0

3 years ago

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What expression can represent 4 more than the product of 6 and 2 1/2

mrs_skeptik [129]

Answer:

6 x 2 1/2 + 4 ??? I hope this is correct :)

Step-by-step explanation:

If its not.. I'm so sorry:(

Have a nice day! <3

7 0

3 years ago

Find the value of x plsss the people that answerd this got it wrong.

liubo4ka [24]

X=145. If its wrong lmk

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2 years ago

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What is the y-coordinate of the midpoint of the line segment of (-4,13) and (18,-3.5)

Nady [450]

The midpoint is (7,4.75) so the y-coordinate should be y=4.75. I hope that helps

4 0

3 years ago

Angle A and angle B are supplementary. The measure of angle B is 82.5.

stealth61 [152]

Answer:

Angle A = 97.5º

Step-by-step explanation:

Supplmentary means 2 angles that equal 180º. So we already have 1 angle, so now all we have to do is subtract 82.5 from 180.

180 - 82.5 = 97.5

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3 years ago

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Find the exterior angle​

Find the exterior angle